Econ 173 Final Assignment
Name: Michael Cooper
December 11, 2024
Effects of Employment on Minimum Wage
Abstract
This report explores the effect of minimum wage on employment and hourly wage, using Ordinary Least Squares regressions and Two-Way Fixed Effects regressions, both with and without state-specific time trends. We find a positive and statistically significant effect of minimum wage on hourly wage, especially for those more likely to be low-skilled workers. However, we do not find a statistically significant effect of minimum wage on employment, even when we filter the data for only those who are likely to experience a binding minimum wage. This includes looking at variables like age, education status, and the occupation or industry that someone works in. Although economic theory suggests a decrease in employment from a binding minimum wage, our results run contrary.
Introduction
Economic theory suggests that there are differing effects on employment from a change in the minimum wage. In this report, we will explore the effects of a non-binding vs. binding minimum wage. To understand the difference between the two, we must first discuss the market-clearing wage. This is the equilibrium wage at which the quantity of labor supplied is equal to the quantity of labor demanded. A non-binding minimum wage would occur if the minimum wage is set below the market-clearing wage. In this scenario, the market wage is already higher than the minimum wage, so there would be no adverse effect. A binding minimum wage would occur if the minimum wage is set higher than the market-clearing wage. At this point, we expect there to be unemployment effects, because less jobs will be available due to the marginal benefit of an additional worker falling below the marginal cost of that worker for many firms. Additionally, the burden of higher wages that firms must pay could be passed onto consumers in the form of higher prices. In this report, we will explore the effects of minimum wage on employment for a variety of different groups that may be more likely or less likely to experience a binding minimum wage.
Econometrics Discussion
In order to study the effect of minimum wage on employment, we will create a difference-in-difference (DD) model, employing a Two-Way Fixed Effects (TWFE) regression. A TWFE regression differs from an OLS regression in that it measures the causal effect of a treatment over time for specific entities, and does not treat all observations as independent. In this case, our TWFE regression measures the effect of minimum wage on employment, controlling for state and time effects. In absence of these trends, we would run into the issue of omitted variable bias, where there are variables excluded from the regression correlated with the minimum wage that could affect employment. For example, more economically prosperous states may have higher minimum wages, and without controlling for state effects, we misattribute the effect of the state’s economic growth on employment to its minimum wage. Similarly, we need to control for trends over time, as the business cycle could be correlated with a state’s minimum wage decisions and could also have an effect on employment. This model can be interpreted as causal under the common trends assumption, which assumes that all states would experience the same employment trends in the absence of minimum wage changes. We can relax this assumption by incorporating a TWFE regression that includes state trends (TWFE + trends). This allows states to have different employment trends in the regression model, which could lead to better results. The minimum wage coefficient in the three models (OLS, TWFE, TWFE + trends) can be interpreted as the percent change in employment rates as a result of a $1 increase in the minimum wage. For the TWFE and TWFE + trends model, this coefficient is the estimated effect relative to the unobserved counterfactual. We can run a hypothesis test on this coefficient by dividing the value by its standard error, and if the value is greater than 1.96, we can reject the null hypothesis that the value is not statistically different from zero. R will automatically calculate this value and assign a special character to values that are statistically significant.
Data Discussion
We will use data from the Current Population Survey (CPS), which is a survey conducted by the Bureau of Census every month which randomly surveys 60,000 households across the United States. Our analysis will focus on survey data collected in the years 2000-2024. This survey gathers important data points for this analysis, including the demographic characteristics of the participants, like age and sex, as well as geographic information, like what state they live in. Additionally, it includes data on hourly and weekly wages. We can then merge this dataset with the state and federal minimum wages over time for each state, replacing the state minimum wage value with the federal minimum wage value if it is lower.
Dataset Descriptive Statistics
| Unique | Missing Pct. | Mean | SD | Min | Median | Max | Histogram | |
|---|---|---|---|---|---|---|---|---|
| year | 25 | 0 | 2011.1 | 6.8 | 2000.0 | 2011.0 | 2024.0 |  |
| age | 49 | 0 | 40.1 | 13.9 | 16.0 | 40.0 | 64.0 |  |
| sex | 2 | 0 | 1.5 | 0.5 | 1.0 | 2.0 | 2.0 |  |
| race | 27 | 0 | 153.8 | 151.2 | 100.0 | 100.0 | 830.0 |  |
| foreign birthplace or parentage | 6 | 0 | 1.8 | 1.5 | 0.0 | 1.0 | 5.0 |  |
| hispanic origin | 15 | 0 | 33.3 | 117.8 | 0.0 | 0.0 | 902.0 |  |
| employed | 2 | 0 | 0.7 | 0.5 | 0.0 | 1.0 | 1.0 |  |
| unemployed | 2 | 0 | 0.0 | 0.2 | 0.0 | 0.0 | 1.0 |  |
| educ_recoded | 11 | 0 | 13.2 | 2.3 | 0.0 | 13.0 | 16.0 |  |
| hourwage_fixed | 6048 | 64 | 15.6 | 9.3 | 0.0 | 13.0 | 100.0 |  |
| earnweek_fixed | 62994 | 39 | 836.9 | 628.7 | 0.0 | 673.0 | 2884.6 |  |
| minwageL | 156 | 1 | 7.3 | 2.0 | 5.2 | 7.2 | 17.0 |  |
| minwageU | 156 | 1 | 7.3 | 2.0 | 5.2 | 7.2 | 17.0 |  |
The summary table shows relevant variable information for the population sample. As you can see the median age in the survey is 40, and the median hourly wage is 13. MinwageL, which is a variable for the lower bound of minimum wage for each state, shows a median of $7.2, which is equivalent to minwageU, the minimum wage upper bound. Additionally, the employed variable shows the percentage of the total population who are employed, which is 70%.
Graph Wage Trends by Region
Figure 1 shows the wage trends in the Northeast census region. As you can see, although the federal minimum wage has remained constant at $7.25 since 2009, there have been strong upward trends for all groups.
Figure 2 depicts the median wage trends for those in the Midwest Census region, which, like in figure 1, shows growth in all wages because the federal wage. The median min wage variable, which is the median state minimum wage for all states included, shows a jump when the federal minimum wage increased, and has since surpassed it. Recently, we see that the median minimum wage is very closely related to the wages for the 18-20 year olds in this region.
Figure 3 depicts wage trends in the South, and while the hourly wage trends for the have all increased, the median minimum wage has remained equal to the federal minimum wage for the southern states.
In Figure 4, we see the wage trends in the West region of the US. In these states, we see that the median hourly wage for those 18-20 has largely coincided with the median minimum wage in the states, suggesting a much greater relationship between minimum wage and median wage for that group than compared to the South and Midwest.
Regress Hourly Wage on State Minimum Wage
| OLS | TWFE | TWFE+trend | |
|---|---|---|---|
| + p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001 | |||
| Minimum wage variable | 1.307*** | 0.152*** | 0.089** |
| (0.046) | (0.036) | (0.030) | |
| Num.Obs. | 2192008 | 2192008 | 2192008 |
| R2 | 0.064 | 0.085 | 0.086 |
In Table 1, we regress hourly wage on state minimum wage. We find in the OLS model with no fixed effects (pooled model) that a $1 increase in the minimum wage is associated with a $1.30 increase in the hourly wage, and is statistically significant. When including the two way fixed effects for state and year, a $1 increase in the minimum is associated with a $0.15 cent increase in hourly wage. When also controlling for state-specific time trends, a $1 increase in minimum wage is associated with a $0.09 increase in hourly wage, and is significant at the 1% level. The effect of minimum wage changes substantially across the regressions and decreases substantially when including the TWFE and state trends. The R-squared values are relatively weak among all of the variables, with the strongest fit in the TWFE + trend regression, which means that the minimum wage explains 8.6% of the variation in hourly wage in the model.
Regress Employment on State Minimum Wage
| OLS | TWFE | TWFE+trend | |
|---|---|---|---|
| + p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001 | |||
| Minimum wage variable | -0.004** | 0.001 | 0.000 |
| (0.001) | (0.001) | (0.001) | |
| Num.Obs. | 5984119 | 5984119 | 5984119 |
| R2 | 0.000 | 0.010 | 0.010 |
Table 2 regresses employment on state minimum wage, and we find a statistically significant effect in the OLS regression of -0.04. However, the R-squared value is zero, and we do not find any statistically significant effects when controlling for state trends and time trends, as well as state-specific time trends. This suggests that the effect of minimum wage on employment for the entire sample is not statistically significant.
Robustness Checks and Alternative Specifications
While exploring the effects of minimum wage on employment and hourly wage for the entire sample could lead to important findings, we will also want to explore groups that are more likely to experience a binding minimum wage. First, We will explore the effect of minimum wage on hourly wage and minimum wage for survey participants who did not complete high school, as their hourly wages and employment status may be more likely to be affected by the minimum wage.
Regress Hourly Wage and Employment on Minimum Wage for those who didn’t finish high school
| Hourly Wage OLS | Hourly Wage TWFE | Hourly Wage TWFE+trend | Employment OLS | Employment TWFE | Employment TWFE+trend | |
|---|---|---|---|---|---|---|
| + p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001 | ||||||
| Minimum wage variable | 0.935*** | 0.224** | 0.199*** | -0.013*** | 0.000 | -0.001 |
| (0.026) | (0.070) | (0.055) | (0.003) | (0.001) | (0.003) | |
| Num.Obs. | 290696 | 290696 | 290696 | 871165 | 871165 | 871165 |
| R2 | 0.103 | 0.135 | 0.137 | 0.002 | 0.017 | 0.017 |
In Table 3, we find a statistically significant effect of minimum wage in all three models, with the TWFE + trends model predicting a 20 cent increase in hourly wage from a $1 increase in minimum wage. However, for the employment effect, we don’t find a statistically significant effect in either model incorporating TWFE. Although the TWFE + trend model results in a coefficient of -0.001, it is not statistically different from 0 at the 10% level. This suggests that increasing the minimum wage has a significant effect on hourly wages for those without a high school degree, but does not affect employment for the group.
Regress Employment on Minimum Wage for 25-54 year olds with at least a Bachelor’s degree and 16-18 year olds
Next, we will explore the effect of minimum wage on employment for 16-18 year olds and 25-54 year olds. 16-18 year olds may be more likely to work in minimum wage jobs and thus experience a binding minimum wage, while 25-54 year olds are less likely to be in those same jobs.
| 16-18 Employment OLS | 16-18 Employment TWFE | 16-18 Employment TWFE+trend | 25-54 Employment OLS | 25-54 Employment TWFE | 25-54 Employment TWFE+trend | |
|---|---|---|---|---|---|---|
| + p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001 | ||||||
| Minimum wage variable | -0.022*** | -0.002 | 0.000 | -0.003* | 0.002+ | 0.000 |
| (0.003) | (0.001) | (0.002) | (0.001) | (0.001) | (0.001) | |
| Num.Obs. | 384984 | 384984 | 384984 | 3783459 | 3783459 | 3783459 |
| R2 | 0.009 | 0.047 | 0.047 | 0.000 | 0.008 | 0.009 |
We find in Table 4 that there is no statistically significant effect of minimum wage on employment for 16-18 year olds in both TWFE effect regression, further supporting the trends we saw in Table 3. Interestingly, the TWFE model without time trends for 25-54 results in a coefficient of 0.002, but it is only significant at the 10% level, and not the 5% level. When controlling for state-specific time trends, this effect goes away, so we conclude there is no effect for either group.
Regress employment on minimum wage for low skilled workers
Like age, industry and occupation can be important determinants in hourly wage, and we can exploit this to find more groups that may experience a binding minimum wage. To find the lowest paying industries, we simply group the data set by industry and calculate the median hourly wage per industry, sorting from lowest to highest. We then include the 10 lowest paying industries in our regression and only include 16–18 year olds.
To find the lowest paying industries, we create an index that divides the median hourly wage per occupation by the minimum wage for each year. The 10 lowest value occupations are included in the regression, excluding tipped workers.
Figure 5 depicts wages over time for the selected occupations, showing similar wages over time that have increased on average.
Regress employment on minimum wage for 16-18 year olds in 10 lowest paying industries
| OLS | TWFE | TWFE+trend | |
|---|---|---|---|
| + p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001 | |||
| Minimum wage variable | 0.008*** | -0.001 | 0.004 |
| (0.001) | (0.003) | (0.004) | |
| Num.Obs. | 48782 | 48782 | 48782 |
| R2 | 0.001 | 0.010 | 0.011 |
Table 5 shows a statistically significant relationship between minimum wage and employment in the OLS regression, predicting an 0.8% increase in employment from a $1 increase in minimum wage. However, the TWFE and TWFE + trends models do not find a statistically significant effect, implying the OLS regression model suffers from omitted variable bias. Table 5 suggests there is no statistically significant effect of minimum wage on employment for 16-18 year olds in the 10 lowest paying industries.
Regress employment on minimum wage for 16-18 year olds in 10 lowest paying occupations
| OLS | TWFE | TWFE+trend | |
|---|---|---|---|
| + p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001 | |||
| Minimum wage variable | 0.005*** | 0.001 | 0.009+ |
| (0.002) | (0.003) | (0.004) | |
| Num.Obs. | 43437 | 43437 | 43437 |
| R2 | 0.001 | 0.010 | 0.011 |
In Table 6, we find that there is a statistically significant relationship in the OLS regression, but it disappears in the TWFE regression. Interestingly, the TWFE + trends regression shows a 0.009 increase in employment from a $1 increase in minimum wage that is statistically significant at the 10% level. However, it is not statistically significant at the 5% level and R-Squared value suggests that minimum wage only explains 1.1% of the variation in employment in the model. We can again conclude that we do not find an effect of minimum wage on employment.
Regress employment on minimum wage for food service workers
Next we will look at 16-18 year old workers that work in the food service industry. These occupations tend to be lower wage and provide an additional group that could experience a binding minimum wage. Like in the Table 6 regression, we exclude tipped workers.
| OLS | TWFE | TWFE+trend | |
|---|---|---|---|
| + p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001 | |||
| Minimum wage variable | 0.008*** | -0.001 | 0.003 |
| (0.001) | (0.004) | (0.005) | |
| Num.Obs. | 27196 | 27196 | 27196 |
| R2 | 0.001 | 0.010 | 0.013 |
Table 7 does not show a statistically significant effect of minimum wage on employment for the TWFE and TWFE + trends models, which is consistent with the previous tables.
Regress employment on minimum wage for 16-18 year old food service industry workers in select states
Finally, we will look at these same works (16-18 in the food service industry) in states where the minimum wage is less than or equal to the federal minimum wage. Perhaps in these states, low wage workers are more likely to be subject to the minimum wage, meaning that they could be more likely to see employment effects from minimum wage increases.
| OLS | TWFE | TWFE+trend | |
|---|---|---|---|
| + p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001 | |||
| Minimum wage variable | 0.020*** | 0.003 | -0.001 |
| (0.003) | (0.026) | (0.023) | |
| Num.Obs. | 16138 | 16138 | 16138 |
| R2 | 0.003 | 0.008 | 0.011 |
Table 8 shows a positive correlation in the OLS regression, but once again there is no causal relationship shown in the TWFE and TWFE + trends models. This suggests that these workers do not experience increased rates of unemployment from increases to the minimum wage.
Conclusion
In conclusion, we find that there are statistically significant effects of the minimum wage on hourly wage, and the effect is greater for low-skilled workers who are more likely to have their wages affected by an increase in the minimum wage. Although economic theory suggests that a binding minimum wage, and subsequent increases to it, should lead to lower levels of employment, we do not find any statistically significant evidence of this from our Difference-in-Difference analysis, where we control for state and time trends, as well as state-specific time trends. This implies labor demand is relatively inelastic, and as employment levels do not change significantly when the minimum wage increases. A potential threat to validity is that minimum wage laws could be correlated with demand shocks, as in times of economic prosperity, states could increase minimum wage laws. In this case, employment may be affected by the economic conditions and not the minimum wage itself, introducing bias. Measurement error could also be present if survey participants misreported their incomes. If the misreporting is random, the results are biased towards zero, which is called attenuation bias. Further research could explore the effects of minimum wage increases on the prices of goods in the area, as that may be another factor that could be affected by a binding minimum wage, as firms may pass their increased costs of labor onto consumers.